Method for time-of-flight estimation of low frequency acoustic signals in reverberant and noisy environment with sparse impulse response

For acoustic procedures which rely on the speed of sound to derive process parameters, the determination of the acoustic time of flight is essential. In this work, a method for the determination of the time of flight (TOF) is presented. It is intended for reverberant and noisy environments and can be applied in the gas holdup determination in bubbly liquids via acoustic transmission tomography (GHATT) for example. The method includes the selection and design of the transmitted signal to optimize the disambiguate of the autocorrelation, the narrowing of the time window based on the Fractional Fourier Transform (FrFT) to accelerate the TOF estimation. Furthermore, it includes the consideration of the system-induced signal distortion through prior quasi-anechoic measurements and the sparse reconstruction of the spatial impulse response for TOF estimation using non-negative sparse deconvolution algorithms. The method is tested analytically on numerically generated signals and various sparse deconvolution algorithms are investigated with respect to their applicability and limitations.

New Explicit Solutions to the Fractional-Order Burgers’ Equation

The closed-form wave solutions to the time-fractional Burgers’ equation have been investigated by the use of the two variables G ′ / G , 1 / G -expansion, the extended tanh function, and the exp-function methods translating the nonlinear fractional differential equations (NLFDEs) into ordinary differential equations. In this article, we ascertain the solutions in terms of tanh , sech , sinh , rational function, hyperbolic rational function, exponential function, and their integration with parameters. Advanced and standard solutions can be found by setting definite values of the parameters in the general solutions. Mathematical analysis of the solutions confirms the existence of different soliton forms, namely, kink, single soliton, periodic soliton, singular kink soliton, and some other types of solitons which are shown in three-dimensional plots. The attained solutions may be functional to examine unidirectional propagation of weakly nonlinear acoustic waves, the memory effect of the wall friction through the boundary layer, bubbly liquids, etc. The methods suggested are direct, compatible, and speedy to simulate using algebraic computation schemes, such as Maple, and can be used to verify the accuracy of results.